Answer to Question #101447 in Mechanics | Relativity for Jude

Question #101447
An archer fires an arrow towards the wall of a castle. The arrow is fired at 45° from horizontal at a velocity of 22m/s. If the wall is 40m away and stands 7m tall, calculate whether the arrow will drop inside the castle walls.

a) Calculate the maximum height of the arrow
b) Calculate the maximum range of the arrow
c) Calculate the vertical height of the arrow as it reaches the wall
d) Describe the journey of the arrow and whether or not it was successful
1
Expert's answer
2020-01-20T05:18:55-0500

"\\alpha =45^{\\circ},\\; v_0=22m\/s, \\; l_0=40m,\\; h_0=7m"

Answers:

a)"h=12.347m"

b)"l=49.387m"

c)"H=7.603m"

d)The arrow will drop inside the castle walls

Explanation:

"x=v_{0x}t, \\; v_{0x}=v_0 \\cos \\alpha"

"y=v_{0y}t-\\frac{gt^2}{2}, \\; v_{0y}=v_0 \\sin \\alpha"

"v_x=v_{0x}, \\; v_y=v_{0y}-gt"


a) Let "t_1" be time point, when the arrow reaches the maximum height.

At this point "v_y=0, \\quad v_0 \\sin \\alpha -gt_1=0, \\quad t_1=\\frac{v_0 \\sin \\alpha}{g}"

"h=v_{0y}t-\\frac{gt^2}{2}=v_0 \\sin \\alpha \\frac{v_0 sin \\alpha}{g} -\\frac{g}{2}(\\frac{v_0 \\sin \\alpha}{g})^2=\\frac{v_0^2{\\sin ^2\\alpha}}{2g}"

"h= \\frac{v_0^2{\\sin ^2\\alpha}}{2g}= \\frac{22^2 * \\frac{1}{2} }{2*9.8} \\approx 12.347m"

b) Let "t_2" be time point, when the arrow reaches the maximum range.

"l=v_{0x} t_2=v_0 \\cos \\alpha \\; 2t_1=v_0 \\cos \\alpha \\; \\frac{2v_0\\sin\\alpha}{g}=\\frac{v_0^2 \\sin 2\\alpha}{g}"

"l =\\frac{v_0^2 \\sin 2\\alpha}{g}=\\frac{22^2 *1}{9.8} \\approx49.387m"

c) Let "t_3" be time point, when the arrow reaches the wall.

"l_0=v_{0x}t_3"

"H=v_{0y}t_3-\\frac{gt_3^2}{2}= v_0 \\sin \\alpha \\frac{l_0}{v_0 \\cos \\alpha} -\\frac{gl_0^2}{2v_0^2 \\cos ^2 \\alpha}= l_0 \\tan \\alpha-\\frac{gl_0^2}{2v_0^2 \\cos ^2 \\alpha}=40*1-\\frac{9.8*40^2}{2*22^2 1\/2}=7.603m"

d) "H>h_0 \\;\\Rightarrow" the arrow will be under the wall


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

Assignment Expert
28.01.20, 20:54

Dear visitor, please use panel for submitting new questions

Jude
28.01.20, 15:58

A 2kg mass is suspended by a 0.25mm diameter copper wire with Young modulus 117GPa. Calculate the extension that will occur if another 1kg mass is added to the 4.87m long wire

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS